The recognition of cancer as a disease caused by the accumulation of genetic alterations has motivated large-scale efforts to annotate the cancer genome for all human cancers. When combined with computational approaches that can distinguish statistically significant, recurrent events from the background noise in high-resolution datasets, these cancer genome surveys yield molecular portraits which are specific for each cancer type and highly consistent across multiple sample sets. In this project, we will link these emerging, large cross-sectional datasets with a novel mathematical model to predict the sequence of genetic events during tumorigenesis. Our predictions will use an evolutionary model of the dynamics within a network of possible mutations. When applied to ~ 70 advanced colorectal cancers, this algorithm correctly reconstructs the sequence of APC -> Ras TP53 mutations previously described for colorectal tumor development. We will first refine our mathematical model to include additional variables such as heterogeneity, epistasls, and differences in the population structure between different tumor types (Aim 1). We will then apply it to genomic datasets for primary glioblastoma (Aim 2) and acute leukemia (Aim 3), predict the sequence of associated genetic events, and examine in mice how the sequence of these genetic events affects tumor formation.